Solve the following inequality. Write the inequality in interval​ notation, and graph it.
7 x plus 5 less than or equals minus 30

According to the intercepts and points, the equation is of the parabola is y = (1/2)*(x + 2 + √2)*(x + 2 - √2)

Equation of the parabola:

The general form of a parabola with the x-intercepts (a, 0) and (b, 0) can be written as:

y = a*(x - a)*(x - b).

Given.

Here we have the x - intercepts (-2 - √2, 0) and (-2  + √2, 0) and the points (-1, 1).

Now, we have to find the equation of the parabola.

Here we know that the x-intercepts are (-2 - √2, 0) and (-2  + √2, 0)

When we apply the values on the general form of the equation of the parabola, then we get the equation as:

=> y = a*(x + 2 + √2)*(x + 2 - √2)

Here we also know that the y-intercept is (-1, 1), which means that when x = -1, we must have y = 1, replacing that we get:

=> 1 = a*(2 + √2)*( 2 - √2)

=> 1 = a*(4 - 2)

=> 1 =  2a

=>  a = 1/2

Therefore, the equation of the parabola is written as,

=> y = (1/2)*(x + 2 + √2)*(x + 2 - √2)

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The number of hours that it will take Alonso to drive 288 miles is 12 hours.

Since Alonso was driving down a road and after 4 hours he had traveled 96 miles, the speed will be:

Speed = Distance / Time

Speed = 96 / 4

Speed = 24 miles per hour.

Therefore, the time taken for 288 miles will be:

Time = Distance / Speed

Time = 288 / 24

Time = 12

The time taken is 12 hours.

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The polynomial expressions are arranged from least to greatest based on their degree as: I, III, II, IV.

The degree of a polynomial expression can be described as the highest exponential power that the terms of a polynomial has.

For example, if we have the polynomial expression that is given as 5x³ + 2x² + 4, the highest power is 3, therefore, the degree of the polynomial is 3.

Thus:

The degree of x + 2xyz is one.

The degree of 9x³y² is three.

The degree of 18x² + 5ab − 6y is two.

The degree of 4x^4 + 3x² − x − 4 is four.

Therefore, from least to greatest, we have: I, III, II, IV.

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Answer:

Step-by-step explanation:

$ 3750  = truck rental;   $125 per ton of sugar transported C is cost;  S is number of tons transported Equation relating C to S would be a linear equation like y = mx + b C = 125S + $3750 This equation would be graphed in the first quadrant only you would start with your y-intercept at (0, 3750) As x increases by 1, your y increases by 125 yielding these points: (1, 3875)  (2, 4000)  (3, 4125)  etc.   

At a z-score of 1.80, the percentage of the scores that are better than yours is equal to 3.59%.

In Mathematics, a z-score is sometimes referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Since a score of 85 on a test corresponds to a z-score of 1.80, the percentage of the scores that are better than yours is given by:

P(x > 85) = P(z > 1.80)

P(z > 1.80) = 0.0359

P(z > 1.80) = 3.59%.

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Answer:

67

Step-by-step explanation:

a+45=112

  -45.  -45

a=67

Hopes this helps please mark brainliest

Answer:

a = 67

Step-by-step explanation:

Given equation,

→ a + 45 = 112

Now the value of a will be,

→ a + 45 = 112

→ a = 112 - 45

→ [ a = 67 ]

Hence, the value of a is 67.

The cost for each pound of almond is $3.25 and the cost of each pound of jelly beans is $1.5.

According to the question,

We have the following information:

For 4 pounds of almonds and 8 pounds of jelly beans, the total cost is $25. For 2 pounds of almonds and 3 pounds of jelly beans, the total cost is $11.

Now, let's take the cost of 1 pound of almond to be $x and that of jelly beans to be $y.

We have the following equations:

4x+8y = 25 ...(1)

2x+3y = 11

2x = 11-3y ...(2)

Putting this value of 2x in equation 1:

2(11-3y)+8y = 25

22-6y+8y = 25

22+2y = 25

2y = 25-22

2y = 3

y = 3/2

y = $1.5

Putting this value of y in equation 2:

2x = 11-3y

2x = 11-3*1.5

2x = 11-4.5

2x = 6.5

x = 6.5/2

x = $3.25

Hence, the cost for each pound of almond is $3.25 and the cost of each pound of jelly beans is $1.5.

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The measure of angle 4 is 121 degrees.

We know that the sum of all angles of triangle is 180 degrees.

∠1 + ∠2 + ∠3 = 180°

81° + 40° + ∠3 = 180°

∠3 = 180° - 121°

∠3 = 59°

We can observe that, angle 3 and angle 4 are linear angles.

So, ∠4 + ∠3 = 180°

∠4 = 180° - ∠3

∠4 = 180° - 59°

∠4 = 121°

Therefore, the measure of angle 4 is 121 degrees.

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The solution of the given one-variable equation as shown in the task content is; Choice B; - 1.25.

It follows from the task content that the solution of the given one-variable equation is to be determined.

Since the given one-variable equation is;

0.7h + 6 = 4 - 0.9h

By adding, 0.9h and subtracting 6 from both sides, we have;

0.7h + 0.9h = 4 - 6

1.6h = -2

h = -2/1.6

h = -1.25

On this note, it follows that the solution of the given equation is; h = -1.25.

Consequently, the answer choice which is correct about the solution of the given equation is; Choice B; - 1.25.

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The altitude of the airplane=300 m

What is altitude?

The height at which something is relative to a planet's or a natural satellite's surface, like sea level or land

The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.

The given figure is a right triangle.

opposite side=x

hypotenuse=500 m

Adjacent side=400 m

According to Pythagoras' theorem,

hypotenuse²=opposite side²+Adjacent side²

500² = x²+400²

2500=x²+1600

x²=2500-1600=900

x=√900=±300

x=300, x=-300

consider positive value

So, the altitude of the airplane=300 m

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Answer:

  x = 10

Step-by-step explanation:

You want the value of x that satisfies x -(x-1)/3 -(2x-5)/5 +(x+8)/6 = 7.

The least common denominator is 5·6 = 30, so we can eliminate the fractions by multiplying by 30:

  30x -10(x -1) -6(2x -5) +5(x +8) = 7·30

  30x -10x +10 -12x +30 +5x +40 = 210 . . . . . eliminate parentheses

  13x +80 = 210 . . . . . . . . . collect terms

  13x = 130 . . . . . . . . . . subtract 80

  x = 10 . . . . . . . . . . divide by 13

__

Additional comment

Often an equation can be nicely solved by a graphing calculator. We like to write the equation in the form f(x) = 0, and look for the x-intercepts. Those are usually labeled by the calculator. Here that rewrite is accomplished by subtracting 7 from both sides.

The time that it take the wevaer to complete 3 1/3 baskets is 5 days.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the weaver completes 2/3 of a basket each day. The time that it will take the wevaer to complete 3 1/3 baskets will be:

= Number of baskets / Number completed daily

= 3 1/3 ÷ 2/3

= 10/3 ÷ 2/3

= 10/3 × 3/2

= 5

It'll take 5 days.

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Answer:

  8/9

Step-by-step explanation:

You want to know the least fraction of the distribution that lies between 61 and 79 if the mean is 70 and the standard deviation is 3.

Chebyshev's inequality tells you that at most 1/k² of the distribution will lie beyond k standard deviations from the mean.

Here, the given limits are (61 -70)/3 = -3 and (79 -70)/3 = 3 standard deviations from the mean. That is, we can use k=3 to find the maximum fraction that is beyond the interval [61, 79]. That fraction is ...

  1/k² = 1/3² = 1/9

Since this is the maximum fraction outside the given range, the minimum fraction inside the given range is ...

  1 -1/9 = 8/9

At least 8/9 of the number are between 61 and 79.

The extra revenue generated by the mail is $2.14 billion

From the question, we have the following parameters that can be used in our solution:

Number of mails in a year = 107 billion pieces

Amount generated per mail = 2¢

From the above parameter, we can calculate the total amount generated using the following equation

The total revenue generated by the mail is calculated as

Amount generated = Number of mails in a year x Amount generated per mail

Substitute the known values in the above equation

So, we have the following equation

Amount generated = 107 billion x 2¢

Evaluate the product

Amount generated = 214 billion ¢

Express as dollars

Amount generated = $ 2.14 billion

Hence, the total amount is $2.14 billion

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The estimated cost of mail per year when the rate of postage is raised by 2¢ is

The problem require conversion of units and multiplication

The extra rate of for raising the postage is given to be 2¢

converting 2¢ to dollars gives $0.02

The rate is used to multiply number o f mails which is 107 billion

107 billion = 107 * 10^9, therefore

107 * 10^9 * 0.02

= 214 * 10^7

= 2.14 * 10^9

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Answer:

y = -30

(0, -30)

Step-by-step explanation:

f(x) = 2(2x - 3) (5x + 5)

2 = 0, 2x - 3 = 0, 5x + 5 = 0

               +3    +3      -5     -5

          ------------------------------

             2x = 3 ,     5x = -5

            ÷2    ÷2      ÷5    ÷5

         --------------------------------

                x = (3/2),   x = -1

f(x) = 2(2(0) - 3) (5(0) + 5)

        2(0 - 3) (0 + 5)

         2(-3) (5)

             -6 × 5 = -30

f(x) = -30

y = -30

(0, -30)

f(x) = 2(2x - 3) (5x + 5)

        2(2(3/2) - 3) (5(3/2) + 5)

        2(3 - 3) (15/2 + 5)

         2(0) (25/2)

y = 0

((3/2), 0))

f(x) = 2(2x - 3) (5x + 5)

        2(2(-1) - 3) (5(-1) + 5)

         2(-2 - 3) (-5 + 5)

          2(-5) (0)

             -10(0)

y = 0

(-1, 0)

I hope this helps!

Answer:

35h+180≤400

Step-by-step explanation:

You multiply 35 by the amount of hours the clown can be at the party (h) and add $180 for the amount of food, which should equate to less than or equal to $400. Hope this helps! :D

Please please PLEASE mark BRAINLIEST!! <3

Answer:

35h+180≤400

I did this question, and I got it correct.

The leaking fruit juice container will get empty in 24.24 minutes

converting 2.5 quart to ounce

1 quart is equivlent to 32 fluid ounce, 2.5 quart will be ?

? = 2.5 * 32

? = 80 fluid ounces

The leakage is at 3.3  fluid ounces per minute to find how many minute it takes to leak 80 fluid ounces we calculate as below

3.3 fluid ounces = 1 minute

80 ounces = ?

cross multiplying gives

= 80 / 3.3

= 24.24 minutes

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The true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

We know that the rational numbers are of the form p/q (i.e., simple fraction) where p, q are integers with q ≠ 0

And an irrational numbers are real numbers that cannot be represented as simple fractions.

An irrational numbers can be written in decimals.

√3 = 1.7321

We know that every terminating decimal is a rational number (for example, 2.5 = 5/2) but every rational number may not be a terminating decimal (for example, 2/3 = 0.666...)

So, a statement 'Every irrational number can be represented as a fraction.' is false.

A statement 'Every irrational number can be represented with the help of decimals.' is True

A statement 'Every rational number can be represented as a terminating decimal.' is False.

and a statement 'Every rational number can be represented as an integer.' is False.

Therefore, the true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

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Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years,

What is an interest rate?

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here, we have

A = P e^(rt) ......(1)

P = Amount Invested = $7000

Interest Rate = 9%

A = Accumulated Amount Double the amount invested = 2P = $14000

t = time in years

from equation (1) , we get

14000 = 7000×e^(0.09)t

2 =  e^(0.09)t

㏑2 = 0.09t

0.6931 = 0.09t

t = 0.6931/0.09

t = 7.7 years

Hence, Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years.

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The graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Given, The function f(x) is graphed in the figure and we have to find the points on the graph representing the relative extreme values

As, we got the extreme values on the graph of a function when the graph makes a turn and the given function graph is turning at two points.

So, the graph has extreme values at two points i.e. b and d

So, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Hence, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

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Answer:

Step-by-step explanation:

so there are square root properties that they want you to recognize and respect :P  everyone wants a little respect,  even the square root sign :D

first we can move things under one root sign, like this...

[tex]\sqrt{10}[/tex] * [tex]\sqrt{6}[/tex] = [tex]\sqrt{10 * 6}[/tex]

now we can do that multiplication under the square root sign.

[tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now we can think about this for a long long time and see that 60 can be split up in other ways besides  10 * 6

for instance 15 * 4  also is  60

so this is equal  [tex]\sqrt{15 * 4}[/tex] = [tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now just take out the perfect square part

2 * [tex]\sqrt{15}[/tex]

this isn't one of the listed answers but it is a correct answer , for what is being asked.   The teacher got the question wrong :o

The arrangement of the fraction from least to greatest is 5/11, 2/3 and 7/8.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers

The fraction can be changed to percentage to make it easier.

7/8 = 7/8 × 100 = 87.5%

5/11 = 5/11 × 100 = 45.5%

2/3 = 2/3 × 100 = 66.7%

The arrangement is 5/11, 2/3 and 7/8.

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The value of 6204 ÷ 4 is 1551

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of it. For example if 30 mangoes are to be shared between 6 students. It shows that 5 mangoes will be given to each student. i.e 30/6= 5

the value of 6204/4 can be obtained by using long division:

4 in 6 gives 1 remainder 2

4 in 22 gives 5 remainder 2

4 in 20 gives 5 remainder 0

4 in 4 gives 1 remainder 0

Therefore the value of 6204/4 = 1551

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Answer: The Answer would be -5 is greater.

Step-by-step explanation: The reason why is that if you had 1 and -2  the 1 would be more because it is not negative.

Answer:

Domain:  (-∞, ∞); Range:  (-∞, -4]

Step-by-step explanation:

Domain is the set of all possible input values of a function (or on a graph, the leftmost and rightmost extensions of the function).

Since this is a parabola, the function will extend left and right for negative infinity and infinity respectively.

Range is the set of all possible output values of a function (or on a graph, the uppermost and lowermost extensions of the function).

While the function on this graph will extend downward for negative infinity, the uppermost limit is -4, as y (output) value of the vertex.

The total volume of 3:12 is 90 gallons  

In math, the term Ratio is used to compare two or more numbers or quantities. It indicates how small or big a quantity is when compared to each other. In a ratio, the comparison between two values is done by using division.  

Here we have    

54 gallons is the volume of 2:7

=> As we know 2+7 = 9

Therefore, for 9 parts = 54 gallons of volume

=> 1 part = 54/9 = 6 gallons of volume

Here we need to find 3: 12

For 3 parts = 3 × 6 gallons of volume = 18 gallons

For 12 parts = 12 × 6 gallons of volume = 72 gallons

=> total volume = 18 gallons + 72 gallons = 90 gallons

Therefore,

The total volume of 3:12 is 90 gallons  

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Answer:

each water is $1.25 each coffee is $1.95

Step-by-step explanation:

we know that the difference between $10.85 and $16.70 is 3 cups of coffee

if we subtract $10.85 from $16.70 we get $5.85

$5.85 divided by 3 is $1.95

so each cup of coffee is $1.95

now we subtract the same $5.85 from the price of 4 waters and 3 coffees

$10.85 minus $5.85 equals $5.00

divide that by 4 to get the price of each water bottle and you get $1.25 per water

The null and alternative hypotheses are H0: µ ≥ 1000 and Ha: µ < 1000 respectively.

The evidence to reject the manufacturer's claim is in the rejection region for the test statistic which is z < -1.54.

The null hypothesis consist of the inequality sign “equal” sign (“=” or “≥” or “≤”).

Alternative hypothesis is the complement to the null hypothesis.

The claim: The mean life of a certain type of light bulb is at least 1000 hours”. At least in inequality is represented by “≥” sign, it is null hypothesis.

H0: µ ≥ 1000

Alternative hypothesis:

The alternative hypothesis is the complement, that is, the mean life of a certain type of light bulb is less than 1000 hours.

Ha: µ < 1000

As the alternative hypothesis contains “<” sign, the test is left-tailed.

Using α = 0.02, we have critical value from standard table of normal distribution:

z0 = -1.54

Therefore, the rejection region for the test statistic is z < -1.54.

Complete question:

A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x x ˉ x, with, \bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a = .02, do you have enough evidence to reject the manufacturer's claim?

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The value of the variable x is,  x = 22.

What is variable in equation?

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. A linear equation with x as a variable and 9 and 4 as constants, for instance, is x+9=4.

Consider, the given equation

√(x - 6) + 2 = 6

Subtract 2 on both sides,

√(x - 6) + 2 - 2 = 6 - 2

          √(x - 6) = 4

Taking square on both sides,

[tex](\sqrt{x-6})^2=4^2\\ (x-6)=16[/tex]

     x - 6 = 16

Add 6 on both sides,

x - 6 + 6 = 16 + 6

           x = 22

Hence, the value of the variable x is x = 22.

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The required coordinates of vertex A' are (3, 4) in the trapezium ABCD.

Trapezium ABCD is given in the question which has :

The coordinates of vertex A is (2, 6)

Here the scale factor is 2

A = (2, 6)

The scale factor of a dilation is given as

k = 2

The center of dilation is given as

Center = (1, 8)

The rule of the dilation is calculated using as

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (1, 8)

k = 2

(x, y) =  (2, 6)

So, we have

A' = (2 × (2 - 1) + 1, 2 × (6 - 8) + 8)

A' = (3, 4)

Hence, the required coordinates of vertex A' are (3, 4).

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The question seems to be incomplete the correct question has been attached